1: *
2: * Definition:
3: * ===========
4: *
5: * SUBROUTINE DGEMQR( SIDE, TRANS, M, N, K, A, LDA, T,
6: * $ TSIZE, C, LDC, WORK, LWORK, INFO )
7: *
8: *
9: * .. Scalar Arguments ..
10: * CHARACTER SIDE, TRANS
11: * INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
12: * ..
13: * .. Array Arguments ..
14: * DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
15: * ..
16: *
17: *> \par Purpose:
18: * =============
19: *>
20: *> \verbatim
21: *>
22: *> DGEMQR overwrites the general real M-by-N matrix C with
23: *>
24: *> SIDE = 'L' SIDE = 'R'
25: *> TRANS = 'N': Q * C C * Q
26: *> TRANS = 'T': Q**T * C C * Q**T
27: *>
28: *> where Q is a real orthogonal matrix defined as the product
29: *> of blocked elementary reflectors computed by tall skinny
30: *> QR factorization (DGEQR)
31: *>
32: *> \endverbatim
33: *
34: * Arguments:
35: * ==========
36: *
37: *> \param[in] SIDE
38: *> \verbatim
39: *> SIDE is CHARACTER*1
40: *> = 'L': apply Q or Q**T from the Left;
41: *> = 'R': apply Q or Q**T from the Right.
42: *> \endverbatim
43: *>
44: *> \param[in] TRANS
45: *> \verbatim
46: *> TRANS is CHARACTER*1
47: *> = 'N': No transpose, apply Q;
48: *> = 'T': Transpose, apply Q**T.
49: *> \endverbatim
50: *>
51: *> \param[in] M
52: *> \verbatim
53: *> M is INTEGER
54: *> The number of rows of the matrix A. M >=0.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The number of columns of the matrix C. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] K
64: *> \verbatim
65: *> K is INTEGER
66: *> The number of elementary reflectors whose product defines
67: *> the matrix Q.
68: *> If SIDE = 'L', M >= K >= 0;
69: *> if SIDE = 'R', N >= K >= 0.
70: *> \endverbatim
71: *>
72: *> \param[in] A
73: *> \verbatim
74: *> A is DOUBLE PRECISION array, dimension (LDA,K)
75: *> Part of the data structure to represent Q as returned by DGEQR.
76: *> \endverbatim
77: *>
78: *> \param[in] LDA
79: *> \verbatim
80: *> LDA is INTEGER
81: *> The leading dimension of the array A.
82: *> If SIDE = 'L', LDA >= max(1,M);
83: *> if SIDE = 'R', LDA >= max(1,N).
84: *> \endverbatim
85: *>
86: *> \param[in] T
87: *> \verbatim
88: *> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
89: *> Part of the data structure to represent Q as returned by DGEQR.
90: *> \endverbatim
91: *>
92: *> \param[in] TSIZE
93: *> \verbatim
94: *> TSIZE is INTEGER
95: *> The dimension of the array T. TSIZE >= 5.
96: *> \endverbatim
97: *>
98: *> \param[in,out] C
99: *> \verbatim
100: *> C is DOUBLE PRECISION array, dimension (LDC,N)
101: *> On entry, the M-by-N matrix C.
102: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
103: *> \endverbatim
104: *>
105: *> \param[in] LDC
106: *> \verbatim
107: *> LDC is INTEGER
108: *> The leading dimension of the array C. LDC >= max(1,M).
109: *> \endverbatim
110: *>
111: *> \param[out] WORK
112: *> \verbatim
113: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
114: *> \endverbatim
115: *>
116: *> \param[in] LWORK
117: *> \verbatim
118: *> LWORK is INTEGER
119: *> The dimension of the array WORK.
120: *> If LWORK = -1, then a workspace query is assumed. The routine
121: *> only calculates the size of the WORK array, returns this
122: *> value as WORK(1), and no error message related to WORK
123: *> is issued by XERBLA.
124: *> \endverbatim
125: *>
126: *> \param[out] INFO
127: *> \verbatim
128: *> INFO is INTEGER
129: *> = 0: successful exit
130: *> < 0: if INFO = -i, the i-th argument had an illegal value
131: *> \endverbatim
132: *
133: * Authors:
134: * ========
135: *
136: *> \author Univ. of Tennessee
137: *> \author Univ. of California Berkeley
138: *> \author Univ. of Colorado Denver
139: *> \author NAG Ltd.
140: *
141: *> \par Further Details
142: * ====================
143: *>
144: *> \verbatim
145: *>
146: *> These details are particular for this LAPACK implementation. Users should not
147: *> take them for granted. These details may change in the future, and are unlikely not
148: *> true for another LAPACK implementation. These details are relevant if one wants
149: *> to try to understand the code. They are not part of the interface.
150: *>
151: *> In this version,
152: *>
153: *> T(2): row block size (MB)
154: *> T(3): column block size (NB)
155: *> T(6:TSIZE): data structure needed for Q, computed by
156: *> DLATSQR or DGEQRT
157: *>
158: *> Depending on the matrix dimensions M and N, and row and column
159: *> block sizes MB and NB returned by ILAENV, DGEQR will use either
160: *> DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
161: *> the QR factorization.
162: *> This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
163: *> multiply matrix Q by another matrix.
164: *> Further Details in DLATMSQR or DGEMQRT.
165: *>
166: *> \endverbatim
167: *>
168: * =====================================================================
169: SUBROUTINE DGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
170: $ C, LDC, WORK, LWORK, INFO )
171: *
172: * -- LAPACK computational routine (version 3.7.0) --
173: * -- LAPACK is a software package provided by Univ. of Tennessee, --
174: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175: * December 2016
176: *
177: * .. Scalar Arguments ..
178: CHARACTER SIDE, TRANS
179: INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
180: * ..
181: * .. Array Arguments ..
182: DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
183: * ..
184: *
185: * =====================================================================
186: *
187: * ..
188: * .. Local Scalars ..
189: LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
190: INTEGER MB, NB, LW, NBLCKS, MN
191: * ..
192: * .. External Functions ..
193: LOGICAL LSAME
194: EXTERNAL LSAME
195: * ..
196: * .. External Subroutines ..
197: EXTERNAL DGEMQRT, DLAMTSQR, XERBLA
198: * ..
199: * .. Intrinsic Functions ..
200: INTRINSIC INT, MAX, MIN, MOD
201: * ..
202: * .. Executable Statements ..
203: *
204: * Test the input arguments
205: *
206: LQUERY = LWORK.EQ.-1
207: NOTRAN = LSAME( TRANS, 'N' )
208: TRAN = LSAME( TRANS, 'T' )
209: LEFT = LSAME( SIDE, 'L' )
210: RIGHT = LSAME( SIDE, 'R' )
211: *
212: MB = INT( T( 2 ) )
213: NB = INT( T( 3 ) )
214: IF( LEFT ) THEN
215: LW = N * NB
216: MN = M
217: ELSE
218: LW = MB * NB
219: MN = N
220: END IF
221: *
222: IF( ( MB.GT.K ) .AND. ( MN.GT.K ) ) THEN
223: IF( MOD( MN - K, MB - K ).EQ.0 ) THEN
224: NBLCKS = ( MN - K ) / ( MB - K )
225: ELSE
226: NBLCKS = ( MN - K ) / ( MB - K ) + 1
227: END IF
228: ELSE
229: NBLCKS = 1
230: END IF
231: *
232: INFO = 0
233: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
234: INFO = -1
235: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
236: INFO = -2
237: ELSE IF( M.LT.0 ) THEN
238: INFO = -3
239: ELSE IF( N.LT.0 ) THEN
240: INFO = -4
241: ELSE IF( K.LT.0 .OR. K.GT.MN ) THEN
242: INFO = -5
243: ELSE IF( LDA.LT.MAX( 1, MN ) ) THEN
244: INFO = -7
245: ELSE IF( TSIZE.LT.5 ) THEN
246: INFO = -9
247: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
248: INFO = -11
249: ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN
250: INFO = -13
251: END IF
252: *
253: IF( INFO.EQ.0 ) THEN
254: WORK( 1 ) = LW
255: END IF
256: *
257: IF( INFO.NE.0 ) THEN
258: CALL XERBLA( 'DGEMQR', -INFO )
259: RETURN
260: ELSE IF( LQUERY ) THEN
261: RETURN
262: END IF
263: *
264: * Quick return if possible
265: *
266: IF( MIN( M, N, K ).EQ.0 ) THEN
267: RETURN
268: END IF
269: *
270: IF( ( LEFT .AND. M.LE.K ) .OR. ( RIGHT .AND. N.LE.K )
271: $ .OR. ( MB.LE.K ) .OR. ( MB.GE.MAX( M, N, K ) ) ) THEN
272: CALL DGEMQRT( SIDE, TRANS, M, N, K, NB, A, LDA, T( 6 ),
273: $ NB, C, LDC, WORK, INFO )
274: ELSE
275: CALL DLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T( 6 ),
276: $ NB, C, LDC, WORK, LWORK, INFO )
277: END IF
278: *
279: WORK( 1 ) = LW
280: *
281: RETURN
282: *
283: * End of DGEMQR
284: *
285: END
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